标题： 神经增强的ALISTA 显示英文标题

标题： Neurally Augmented ALISTA

摘要： 众所周知，许多迭代稀疏重建算法可以展开以得到一个可学习的神经网络，从而提高经验性能。 一个典型的例子是学习型迭代软阈值算法（LISTA），其中权重、步长和阈值从训练数据中学习。 最近，分析型LISTA（ALISTA）被引入，结合了完全学习方法（如LISTA）的强大经验性能，同时保留了经典压缩感知算法的理论保证，并显著减少了需要学习的参数数量。 然而，这些参数是在期望下进行训练的，常常导致个体目标的重建效果不佳。 因此，在这项工作中，我们引入了神经增强型ALISTA，其中在重建过程中使用LSTM网络为每个目标向量分别计算步长和阈值。 这种自适应方法的理论依据是对ALISTA的恢复保证进行了重新审视。 我们证明，我们的方法进一步提高了稀疏重建的经验性能，特别是在压缩比更具挑战性时，超越现有算法的差距越来越大。 显示英文摘要

摘要： It is well-established that many iterative sparse reconstruction algorithms can be unrolled to yield a learnable neural network for improved empirical performance. A prime example is learned ISTA (LISTA) where weights, step sizes and thresholds are learned from training data. Recently, Analytic LISTA (ALISTA) has been introduced, combining the strong empirical performance of a fully learned approach like LISTA, while retaining theoretical guarantees of classical compressed sensing algorithms and significantly reducing the number of parameters to learn. However, these parameters are trained to work in expectation, often leading to suboptimal reconstruction of individual targets. In this work we therefore introduce Neurally Augmented ALISTA, in which an LSTM network is used to compute step sizes and thresholds individually for each target vector during reconstruction. This adaptive approach is theoretically motivated by revisiting the recovery guarantees of ALISTA. We show that our approach further improves empirical performance in sparse reconstruction, in particular outperforming existing algorithms by an increasing margin as the compression ratio becomes more challenging.